Algorithms for leader selection in large dynamical networks: Noise-free leaders

• Published in: 2011 50th IEEE Conference on Decision and Control and European Control Conference pp. 7188 - 7193
• Main Authors: Fardad, M., Fu Lin, Jovanovic, M. R.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2011
• Subjects: Approximation algorithms; Consensus; convex optimization; convex relaxation; effective resistance; Greedy algorithms; Kron reduction; Laplace equations; Lead; leader selection; Linear approximation; Optimization; semidefinite programing; sparsity; Vectors; ℓ 1 minimization
• ISBN: 9781612848006; 1612848001
• ISSN: 0191-2216
• DOI: 10.1109/CDC.2011.6161482

We consider networks of single-integrator systems, where it is desired to optimally assign a predetermined number of systems to act as leaders. Performance is measured in terms of the ℋ 2 norm of the overall network, and the leaders are assumed to always follow their desired state trajectories. We demonstrate that, after applying a sequence of relaxations, the problem can be formulated as a semidefinite program and thus solved efficiently. We compare the results of our algorithms against others reported in the literature. Finally, we interpret the leader selection problem in terms of electrical networks and Kron reduction theory.